Question

Use the point on the line and the slope of the line to find three additional points that the line passes through. (There is more than one correct answer.) $$ \frac{\text { Point }}{(-2,-2)} \quad \frac{\text { Slope }}{m=2} $$

Short answer

Three additional points on the line are (-1, 0), (0, 2), and (1, 4).

Step-by-step solution

Understanding the Slope

Firstly, it's crucial to understand that the slope of a line is the amount that y increases (or decreases if the slope is negative) for each increase of 1 in x. It implies that if you move 1 unit to the right (increase x by 1), y will increase by the amount of the slope. In this case, the slope is 2, so y will increase by 2 for each increase of 1 in x.

Finding the first point

Begin with the given point (-2, -2). Increase the x-coordinate (x1) by 1 to find x2, so x2 = -2 + 1 = -1. As the slope is 2, increase the y coordinate (y1) by 2 to find y2, so y2 = -2 + 2 = 0. Thus, the first new point is (-1, 0).

Finding the second point

Start with the new point (-1, 0). Again, increase the x-coordinate (-1) by 1 to find x2, so x2 = -1 + 1 = 0. Increase the y coordinate (0) by 2 (the slope) to find y2, so y2 = 0 + 2 = 2. Thus, the second new point is (0, 2).

Finding the third point

Start with the new point (0, 2). Once more, increase the x-coordinate (0) by 1 to find x2, so x2 = 0 + 1 = 1. Increase the y coordinate (2) by 2 (the slope) to find y2, so y2 = 2 + 2 = 4. Thus, the third new point is (1, 4).